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 Test Your Intuition about the AlonTarsi Conjecture
 Thilo Weinert: Transfinite Ramsey Numbers
 Timothy Chow Launched Polymath12 on Rota Basis Conjecture and Other News
 Proof By Lice!
 The seventeen camels riddle, and Noga Alon’s camel proof and algorithms
 Edmund Landau and the Early Days of the Hebrew University of Jerusalem
 Boolean Functions: Influence, Threshold, and Noise
 Laci Babai Visits Israel!
 Polymath10 conclusion
Top Posts & Pages
 Answer: Lord Kelvin, The Age of the Earth, and the Age of the Sun
 A Breakthrough by Maryna Viazovska Leading to the Long Awaited Solutions for the Densest Packing Problem in Dimensions 8 and 24
 Extremal Combinatorics IV: Shifting
 Greg Kuperberg: It is in NP to Tell if a Knot is Knotted! (under GRH!)
 Test Your Intuition about the AlonTarsi Conjecture
 Can Category Theory Serve as the Foundation of Mathematics?
 Noise Stability and Threshold Circuits
 Updates and plans III.
 Polymath 10 Emergency Post 5: The ErdosSzemeredi Sunflower Conjecture is Now Proven.
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Category Archives: Open discussion
Why is Mathematics Possible: Tim Gowers’s Take on the Matter
In a previous post I mentioned the question of why is mathematics possible. Among the interesting comments to the post, here is a comment by Tim Gowers: “Maybe the following would be a way of rephrasing your question. We know … Continue reading
Posted in Open discussion, Philosophy, What is Mathematics
Tagged Foundations of Mathematics, Open discussion, Philosophy, Tim Gowers
23 Comments
Why is mathematics possible?
Spectacular advances in number theory Last weeks we heard about two spectacular results in number theory. As announced in Nature, Yitang Zhang proved that there are infinitely many pairs of consecutive primes which are at most 70 million apart! This is a sensational achievement. … Continue reading
Polynomial Hirsch Conjecture 5: Abstractions and Counterexamples.
This is the 5th research thread of polymath3 studying the polynomial Hirsch conjecture. As you may remember, we are mainly interested in an abstract form of the problem about families of sets. (And a related version about families of multisets.) The … Continue reading
Polymath3: Polynomial Hirsch Conjecture 4
So where are we? I guess we are trying all sorts of things, and perhaps we should try even more things. I find it very difficult to choose the more promising ideas, directions and comments as Tim Gowers and Terry Tao did so … Continue reading
Posted in Combinatorics, Convex polytopes, Open discussion, Open problems, Polymath3
Tagged Hirsch conjecture, Polymath3
74 Comments
Polymath3 : Polynomial Hirsch Conjecture 3
Here is the third research thread for the polynomial Hirsch conjecture. I hope that people will feel as comfortable as possible to offer ideas about the problem we discuss. Even more important, to think about the problem either in the directions suggested by … Continue reading
Posted in Combinatorics, Convex polytopes, Open discussion, Open problems, Polymath3
Tagged Polymath3
102 Comments
Polymath 3: The Polynomial Hirsch Conjecture 2
Here we start the second research thread about the polynomial Hirsch conjecture. I hope that people will feel as comfortable as possible to offer ideas about the problem. The combinatorial problem looks simple and also everything that we know about it is rather simple: … Continue reading
Posted in Convex polytopes, Open discussion, Open problems, Polymath3
Tagged Hirsch conjecture, Polymath3
104 Comments
Polymath 3: Polynomial Hirsch Conjecture
I would like to start here a research thread of the longpromised Polymath3 on the polynomial Hirsch conjecture. I propose to try to solve the following purely combinatorial problem. Consider t disjoint families of subsets of {1,2,…,n}, . Suppose that … Continue reading
Posted in Convex polytopes, Open discussion, Open problems, Polymath3
Tagged Hirsch conjecture, Polymath3
120 Comments
Polymath Reflections
Polymath is a collective open way of doing mathematics. It started over Gowers’s blog with the polymath1 project that was devoted to the Density Hales Jewett problem. Since then we had Polymath2 related to Tsirelson spaces in Banach space theory , an intensive Polymath4 devoted … Continue reading
When It Rains It Pours
After our success in exploring the phrase “more or less” in many languages here is a task of a similar nature There is a saying in Hebrew: “Troubles come in packages” צרות באות בצרורות “Tzarot Baot bitzrorot”. I am curious about analogs in other … Continue reading
The Polynomial Hirsch Conjecture: Discussion Thread, Continued
Here is a link for the justposted paper Diameter of Polyhedra: The Limits of Abstraction by Freidrich Eisenbrand, Nicolai Hahnle, Sasha Razborov, and Thomas Rothvoss. And here is a link to the paper by Sandeep Koranne and Anand Kulkarni “The dstep Conjecture is Almost true” – … Continue reading
Posted in Convex polytopes, Open discussion, Open problems
Tagged Convex polytopes, Hirsch conjecture
16 Comments